(In reply to
computer solution by Charlie)
Nice list. A quick scan shows that there are not only triples with the same number of divisors but also quartets: 242, 243, 244, 245 and a few others. (none of semiprimes, or course.) An additional OEIS sequence would be appropriate.
I didn't notice any quintets. Care to search further?
Looking at the number of factors column, there are of course no odds. Also no 10 which isn't too surprising  you'd need 3 consecutive numbers with factors that are 4th powers.

Posted by Jer
on 20140418 14:08:50 